Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.
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1 Chapter 6 Review Geometry Name Score Period Date Solve the proportion = m 1 3m 4 m = n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? and 6 4. If =, then = 9 y x? 5. Is NPQR similar to VUTS? If yes, Explain why 6. PQR is similar to LMN. a) Find the scale factor of PQR to LMN b) Find the value of x. c) Find the value of y. d) Find the value of z x = y = z = 7. Find the length of RQ. 8. Find the value of y. y =
2 9. Are the triangles to the right similar? If yes, a) Explain why and b) Write a similarity statement 10. Are the triangles to the right similar? If yes, a) Explain why and b) Write a similarity statement 11. Find the value of a. a = 12. A rectangular swimming pool has dimensions of 30 ft wide and 50 ft long. The rectangular fence around the pool is similar to the shape of the pool. The fence is 45 ft wide. Find the length of the fence. Length =
3 13. Find the value of x. x = A 12 C 4 B x 18 E D
4 Chapter 7 / Review Pythagorean theorem: c 2 = a 2 + b 2, where a and b are the measures of the length of the 2 legs of the right triangle and c is the measure of the hypotenuse. 1. What is the longest side of a right triangle called? 2. What is the length of the hypotenuse of a right triangle with leg lengths of 3 in. and 4 in.? A. 5 inches B. 9 inches C. 16 inches D. 25 inches 3. Find the length of r. r = 4. Find the length of h. h = 5. Find the height and the area of the isosceles triangle below. h = Using the converse of the Pythagorean theorem Area = If the square of the longest side is equal to the sum of the squares of the 2 other legs of the triangle, then the triangle is a right triangle. 6. Is PYT a right triangle? (yes/no) = 7. Classify the triangle formed by the side lengths 14, 21, and 25 as acute, right, or obtuse. The geometric mean between 2 numbers is the square root of their product. x = ab, where a and b are the 2 numbers and x is the geometric mean. Find the geometric mean of the following pairs of numbers. a. 4, 9 b. 16, 5 c. 12, 16
5 Theorem 7-2: If an altitude is drawn from one vertex of a right angle of a right triangle to its hypotenuse, then the 2 triangles formed are similar to the given triangle and to each other. The measure of this altitude is the geometric mean between the measures of the two segments of the hypotenuse. Moreover, the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to that leg. Practice the examples below and apply these theorems. 8. Identify the three similar right triangles in the diagram to the right. 9. Find the length of x. x = 10. Find the length of x. x = ===================================================== A triangle is the only isosceles right triangle. The hypotenuse is 2 times as long as a leg, so the ratio of the sides is 1:1: 2. A triangle also has special properties. The measures of the sides are x, x 3, and 2x, giving the sides a ration of 1: 3 :2. If you see these special triangles, you do not have to use the Pythagorean theorem to find the sides of the right triangle. 7.4 Find the value of each variable
6 7.5 Find tan A and tan B. Write each answer as a fraction. You might want to use, SOH CAH TOA, to remember the trigonometric ratios of the sides of a triangle given an angle. These ratios help you find angles and sides of a right triangle Use a tangent ratio to find the value of x. Round your answer to the nearest tenth Use a sine or cosine ratio to find the value of each variable. Round to nearest tenth Solve a right triangle by finding all the angles and sides of the triangle given. Round your answer to the nearest tenth. Remember that to find the angles, you must use the trigonometric inverses. When you use your graphing calculator, use the second button before you press the cos, sin, or tan A 30- foot tree casts a 12- foot shadow. Find the angle of elevation from the end of the shadow on the ground to the top of the tree (to the nearest tenth of a degree). Angle of Elevation =
7 Chapter 8 / Review 1. What is the sum of the measures of the exterior angles of an octagon? What is the sum of the measures of the interior angles of a decagon? The sum of the measures of the interior angles of a polygon is 720º. 3. How many sides does the polygon have? 4. Find the value of x. x = 5. Find the value of x. x = 6. Find the value of x. x = 7. Find the value of x and y. x = y = 8. Find the value of x and y. x = 9. Find the value of h and k. h = y = k = 10. Find the value of x and y. x = y =
8 11. Find the value of x and y. x = y = 12. Find the measures of L, J, M. L = J = M = 13. Find the value of x. x = 14. Find the measures of V and T. V = T = True or False 13. Diagonals are congruent in a rectangle and a square All angles are congruent in a square and a kite All sides are congruent in a parallelogram Base angles are congruent in an isosceles trapezoid All angles and sides are congruent in a rhombus Diagonals bisect each other in a parallelogram. 18.
9 Chapter 10 Review Geometry Name Period Date Use the diagram to match the notation with the term that best describes it Find the value of x. 9. Find the value of r. (Point B and D are points of tangency) 10. AC and BE are diameters of circle F. Find the measure of the arcs: a. = c. = b. = d. = 11. Find the value of x. 12. Find the value of x.
10 13. The measure of arc AC = 150 º 14. Find the measure of Find the measure of arc AB 15. Find the measure of LNM 16. Find the measure of x and y. x = Find the measure of arc LN y = 17. Line t is tangent to the circle. 18. Find the value of x. Find the measure of 19. Find the value of x. 20. Find the value of x. 21. Find the value of x. 22. Find the value of x.
11 Chapter 11 Review Name Period Date For each problem, write the area formula and show all of your work. Make sure to label your answer with the appropriate unit of measure. 1. Find the area. 2. Find the area. Geometry 3. Find the area. 4. Find the area. 5. Find the area. 6. Area = 415 ft 2. h = 3 9 f t h 2 4 f t 7. Area = 120 ft 2 x = 8. Area = 24 yd 2 x = x 9 ft. 9. JKL XYZ Find the length of side XY
12 10. The ratio of the areas of two trapezoids is 81:25. Write the ratio of the lengths of the corresponding sides. 11. Find the circumference of a circle with radius 5.5 inches. 12. Find the area of a circle with radius 8.1 ft. 13. Find the diameter of a circle with C = 74 ft. 14. Find the arc length of AB. 15. Find the length of radius AQ. 16. Find area of the shaded sector. 17. Find area of the regular polygon Find the probability that a point W, selected randomly on PQ, is on the segment PR. 19. Find the probability that a randomly selected point lies on the shaded region.
13 Chapter 12 Review For Final 1. Find the number of faces, vertices, and edges of the polyhedron below. Faces, Vertices, Edges 2. Find the surface area. 3. Find the surface area. 4. Find the surface area. 5. Surface Area = 717 in 2. Find x. 6. Find the volume. 7. Find the volume. 8. Find the volume. 9. Volume = 72 ft 3. Find x.
14 10. Find the surface area and volume. S = V = 11. Determine whether the solids below are similar. Be sure to explain your answer. 12. Solid A (shown) is similar to Solid B (not shown). The scale factor is 1: 3. Find the surface area S and volume V of Solid B. S = V =
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For math conventions used on the GRE, refer to this link:
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